Would others on this forum consider this to be an IDB? The other question for the forum: is the pet embargo an AA/AE generated thing or is there something else to it? It seems to me that, assuming the OP is being forthright about their history and situation, AA/AE might want to make an exception just to solve the problem.
Also, OP... a couple questions. If you were willing/able to check your dog, could you have gotten out? And secondly, did you explore other options for getting out such as flying AC or Carribean Airlines?